in this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group g and give four equivalent conditions each ofwhich characterizes this relation. we demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. moreover, we study the behavior of these equivalence classes under theaction of a...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

Let μ be a rational-valued metric on a finite set T . We consider (a version of) the multifacility location problem: given a finite set V ⊇ T and a function c : V2 ) → Z+, attach each element x ∈ V − T to an element γ(x) ∈ T minimizing ∑(c(xy)μ(γ(x)γ(y)) : xy ∈ V2 ) ), letting γ(t) := t for each t ∈ T . Large classes of metrics μ have been known for which the problem is solvable in polynomial t...

The partial inverse minimum cut problem is to minimally modify the capacities of a digraph such that there exists a minimum cut with respect to the new capacities that contains all arcs of a prespecified set. Orlin showed that the problem is strongly NP-hard if the amount of modification is measured by the weighted L1-norm. We prove that the problem remains hard for the unweighted case and show...

we introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. we firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. we next argue about the strong$alpha$-reversibility of some kinds of extensions. a number ofproperties of this version are established. it is shown ...

The aim of this paper is to study the properties of t-cut set, strong t-cut set, t-quasi-cut set, strong t-quasi-cut set and ∈ ∨q-cut set of a fuzzy set μ. For any intuitionistic fuzzy A =< μA, νA > and α, β ∈ [0, 1], we define and study the properties of upper (α, β) cut setA(α,β), strong upper (α, β) cut setA(α, β) ̇ , lower (α, β) cut set A, strong lower (α, β) cut set A (α, β) ̇ , upper (α, β...